An emerging answer to Seed's question

I want people to understand that there is no law of averages. There are no laws of probability (at least not if you mean something like "Really improbable things don't happen"). You can't prove just anything with statistics.

My inclination would actually have been phrased the exact opposite way, though getting at the same point.

It's true that there's no law which says that a head is more likely when you've flipped several tails in a row, there are indeed laws of probability. They belong to a whole class of things which many people have a lot of trouble with: emergent properties.

Emergent properties rely on large numbers and often on interactions between simple agents. Out of that large number of interactions, complex and often predictable results emerge. A probability or an average is a very simple emergent property of a system. Biological fitness can be expressed as such a simple probability. Natural selection is a result of multiple organisms with different fitnesses interacting with an environment, and the trend we can find in natural selection – its predictive capability – is also an emergent process.

Evolution is a combination of natural selection and a number of probabilistic (and therefore emergent) processes, all of which combine to produce the complex system of life on Earth that we know.

An organism's life is itself an emergent property of the successful interactions of numerous cells, each of which has numerous interacting molecular agents within it. The mind can be seen as an emergent process of the neurons in the brain. Individual neurons follow very simple rules, but it seems that when you get enough of them together, truly wondrous things emerge.

Anthills and ecosystems are emergent processes, too.

Most of the challenges we face in modern society relate to our ability to manage the complexity of these sorts of processes. Often as not, there is a probabilistic component to these processes, which requires that we appreciate the real laws of probability. The extinction of one species, a small change in carbon dioxide emissions, or the accumulation of numerous small mutations can have dramatic effects, and those effects are predictable and understandable when we appreciate how the emergent process works.

When confronted with these sorts of situations, most people just get hung up on the complexity. The atmosphere is a complex, feedback driven system. Emergence tells us that predictable simplicity can arise from such systems, and that's why climate modelers can do their work and produce a basic agreement about the effects of rising carbon dioxide. If more policy-makers appreciated that, we might be closer to controlling that change.

Evolution is complicated. It's built around the complexity of each organism, and a complex set of unpredictable changes in the environment and the organism's genetic code. But out of those numerous interactions, a predictable process emerges. If more biology teachers, let alone parents, school boards and voters, appreciated how evolution emerges from that complexity, a lot of the creationism battles would go away.

Lack of appreciation of emergence is behind many divisive social issues of the day, and if I could shake that into a few more minds, I'd be a happy man.